What are some of the problems that tended to exist in newly independent nations that experienced a long period of colonial rule?
There tend to be two major types of problems that affect such countries.
First, there are economic problems. These countries tend to have been run (economically speaking) for the benefit of their colonizer. This tends to mean that they do not have economies that are well-suited for independence. This typically makes them poor and makes them continue to depend on rich nations economically.
Second, there are political problems. These countries have not typically been allowed to be democratic. The colonizer tends to use a few native elites to rule the country and the colonizer tends to only care that order be maintained. Colonizers do not want true democracy, with all its messiness. Therefore, the native people do not learn how to be democratic. Then they are made independent all of a sudden. At that point, the ruling class tends to become kleptocratic and power hungry. This prevents the country from becoming truly democratic.